Small Engines (Lawn Mowers, etc.): John Deere GT275 stalling when hot, squirt bottle, maintenance records

Question
Hi.  I have a John Deere GT275 mower that I bought second hand.  The previous owner was very good with keeping maintenance records etc, and seemed to keep the mower well maintained.  It was made in 1996, but had a new engine installed in 2001 - Kawasaki 17hp.  

Later last year I started to have problems with it stalling when it got hot, usually after mowing for about 45 minutes.  I have brought it in to 2 different shops, both seem stumped, and neither have been able to replicate the problem, or even give me suggestions how to trouble shoot it.  It happens very consistently for me know, almost every time I mow.  

I'm not real familiar with small engines, so can you give me some ideas as to what I can look at or trouble shoot when the problem comes up again?  Thank you very much for any help or suggestions you can give.  

Answer
Hiya Mark-
Gotta tell ya, I'm NOT a fan of these Kawasakies their puttin on.

sigh- anyways, do this.  Small squirt bottle with gas, remove air cleaner, run it til it begins to stall, squirt in some gas.  If it picks back up- fuel pump problem, it it dosen't you need a new ignition module.

Give that a try lemme know what it does.
CYA!